Finite Group Databasebeta

← #25302696

Subgroups — #25302696

Order 11008.

4086 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583444C216yesmaximal, complemented
2#19142992C211yesmaximal, characteristic, complemented
3#19142989C211yesmaximal, characteristic, complemented
4#19142949C216yesmaximal, complemented
5#19142940C211yesmaximal, characteristic, complemented
6#19142938C216yesmaximal, complemented
7#127×Dic43C211yesmaximal, characteristic, complemented
8#19137159C216yesmaximal, complemented
9#19137157C211yesmaximal, characteristic, complemented
10C2×C42×Dic43C211yesmaximal, characteristic, complemented
11C43×#2856C211yesmaximal, characteristic, complemented
12C22×#10621900C2214yes—
13#14583444—248no—
14C2×#13063324C2216yes—
15C2×#13063322C2211yescharacteristic
16C2×#13063321C2216yes—
17C2×#13063321C2216yes—
18C2×#13063311C22112yes—
19C2×#13063299C2216yes—
20C2×#13063297C22112yes—
21C2×D4×Dic43C2216yes—
22C2×#13063287C2216yes—
23C2×(C22⋊D43)⋊C4C22112yes—
24C22×C4×Dic43C2213yes—
25C22×C4×Dic43C2213yes—
26#14582802C2216yes—
27#14582801C2216yes—
28#14582800C2216yes—
29#14582799C22124yes—
30#14582769C2211yescharacteristic
31#14582768C2216yes—
32C42×Dic43C2213yes—
33C42×Dic43C2211yescharacteristic
34C42×Dic43C2211yescharacteristic
35C42×Dic43C2213yes—
36C2×#127×C43C2211yescharacteristic
37C2×#121×C43C2216yes—
38C22×C42×C43C2211yescharacteristic
39C43×#390C2216yes—
40C43×#384C2211yescharacteristic
41C2×#10621900—248no—
42C22×Dic86C2314yes—
43C22×D172C2316yes—
44C22×C22⋊D43C23112yes—
45C22×C22⋊D43C2314yes—
46C22×C22⋊D43C2314yes—
47C23×Dic43C2314yes—
48C23×Dic43C2313yes—
49C23×Dic43C2311yescharacteristic
50C22×C4×D43C2314yes—
51#13063324—224no—
52#13063322—24no—
53#13063321—224no—
54#13063321—224no—
55#13063311—248no—
56#13063299—224no—
57#13063297—248no—
58D4×Dic43—224no—
59#13063287—224no—
60(C22⋊D43)⋊C4—248no—
61C2×C4⋊Dic43C2316yes—
62C2×Dic43⋊C4C23112yes—
63C2×C22⋊Dic43C23112yes—
64C2×(C2×D43)⋊C4C23112yes—
65C2×(C2×D43)⋊C4C23112yes—
66C2×C4×Dic43—212no—
67C2×C4×Dic43D4124yescomplemented
68C2×C4×Dic43C2316yes—
69C2×C4×Dic43C2313yes—
70C2×C4×Dic43C2313yes—
71C2×C4×Dic43C2313yes—
72C2×C4×Dic43C2313yes—
73C2×C4×Dic43C2313yes—
74C2×C4×Dic43C2313yes—
75C22×D4×C43C2316yes—
76C22×D4×C43C2314yes—
77C23×C4×C43C2313yes—
78#127×C43—24no—
79#121×C43—224no—
80C2×C4⋊C4×C43C2316yes—
81C2×C22⋊C4×C43C23112yes—
82C2×C42×C43—24no—
83C2×C42×C43C2313yes—
84C2×C42×C43C2311yescharacteristic
85C24×C43C2414yes—
86C24×C43C2411yescharacteristic
87C23×D43C2414yes—
88C2×D4×C43—212no—
89C2×D4×C43—212no—
90C2×D4×C43—212no—
91C2×D4×C43—224no—
92C22×C4×C43—26no—
93C22×C4×C43—26no—
94C22×C4×C43C2×D4112yes—
95C22×C4×C43C2414yes—
96C22×C4×C43C2413yes—
97C22×C4×C43C2413yes—
98C2×C22⋊D43—224no—
99C2×C22⋊D43—224no—
100C2×C22⋊D43—248no—
101C2×C22⋊D43—224no—
102C22×Dic43—212no—
103C22×Dic43—224no—
104C22×Dic43C2×D4112yes—
105C22×Dic43C2×D4112yes—
106C22×Dic43C2414yes—
107C22×Dic43C2413yes—
108C22×Dic43C2411yescharacteristic
109C22×Dic43C2411yescharacteristic
110C22×Dic43C2413yes—
111#10621900—464no—
112C2×D172—212no—
113C2×D172—212no—
114C2×D172—212no—
115C2×C4×D43—224no—
116C2×Dic86—224no—
117C4⋊C4×C43—212no—
118C22⋊C4×C43—224no—
119C42×C43—26no—
120C42×C43#4114yescomplemented
121C22⋊Dic43—224no—
122(C2×D43)⋊C4—224no—
123(C2×D43)⋊C4—224no—
124C4⋊Dic43—212no—
125Dic43⋊C4—224no—
126C4×Dic43—26no—
127C4×Dic43—212no—
128C4×Dic43C2×D4112yes—
129C4×Dic43C2×D4112yes—
130C4×Dic43C2×D4112yes—
131C4×Dic43C2×D4112yes—
132C4×Dic43#41112yescomplemented
133C23×C43—23no—
134C23×C43—21no—
135C23×C43—212no—
136C23×C43—212no—
137C23×C43—24no—
138C23×C43C22×D416yes—
139C23×C43C2511yescharacteristic
140C22×D43—212no—
141C22×D43—24no—
142C22×D43—212no—
143D4×C43—416no—
144D4×C43—424no—
145C2×C4×C43—23no—
146C2×C4×C43—23no—
147C2×C4×C43—224no—
148C2×C4×C43—212no—
149C2×C4×C43C22×D416yes—
150C2×C4×C43C22×D416yes—
151C2×C4×C43C2×#4116yes—
152C2×C4×C43C2×#4116yes—
153C22⋊D43—416no—
154C22⋊D43—416no—
155C22⋊D43—448no—
156C2×Dic43—26no—
157C2×Dic43—224no—
158C2×Dic43—212no—
159C2×Dic43—416no—
160C2×Dic43#127116yescomplemented
161C2×Dic43C22×D416yes—
162C2×Dic43C22×D416yes—
163C2×Dic43C22×D416yes—
164C2×Dic43C22×D416yes—
165C2×Dic43C2×#41112yes—
166D172—424no—
167C4×D43—416no—
168Dic86—416no—
169#36644—431nomaximal, Sylow
170C22×C43—26no—
171C22×C43—26no—
172C22×C43—44no—
173C22×C43—412no—
174C22×C43—412no—
175C22×C43C2×#12714yes—
176C22×C43C23×D413yes—
177C22×C43C22×#4113yes—
178C22×C43C22×#4111yescharacteristic
179C2×D43—44no—
180C2×D43—412no—
181C2×D43—412no—
182C4×C43—26no—
183C4×C43—44no—
184C4×C43#532112yescomplemented
185Dic43—26no—
186Dic43—44no—
187Dic43C2×#12714yes—
188Dic43C2×#12714yes—
189Dic43#532112yescomplemented
190C2×#532—436no—
191#2868—431no—
192#2867—431no—
193#2858—436no—
194#2856—431no—
195#2856—436no—
196#2856D4311yescharacteristic, complemented
197C4×#127—436no—
198C4×#127—431no—
199C4×#127—431no—
200C2×C43—431no—
201C2×C43—24no—
202C2×C43—84no—
203C2×C43C22×#12711yescharacteristic
204C2×C43C2×#53213yes—
205C2×C43C2×#53213yes—
206D43—84no—
207C22×#41—434no—
208#532—8648no—
209C2×C4⋊Q8—436no—
210C2×#127—436no—
211C2×#127—436no—
212C2×#127—431no—
213C2×#127C2×D4311yescharacteristic
214C2×#124—4312no—
215C2×#121—4312no—
216C2×#121—436no—
217C2×#121C2×D4316yes—
218C2×C4×D4—436no—
219C2×C4×D4—436no—
220C2×C4×D4—4312no—
221C22×C42—433no—
222C22×C42—433no—
223C22×C42C2×D4311yescharacteristic
224#390—436no—
225#390—436no—
226#390—4324no—
227#390—436no—
228#390C2×D4316yes—
229#384—436no—
230#384—431no—
231#384C2×D4311yescharacteristic
232C43—433no—
233C43—431no—
234C43—433no—
235C43—431no—
236C43#3664411yescharacteristic, complemented, Sylow
237C2×#41—8648no—
238C22×Q8—434no—
239C22×D4—4312no—
240C22×D4—434no—
241C22×D4—434no—
242C22×D4—436no—
243C22×D4C22×D4316yes—
244C22×D4C22×D4314yes—
245C23×C4—431no—
246C23×C4—433no—
247C23×C4—434no—
248C23×C4—434no—
249C23×C4C22×D4313yes—
250C4⋊Q8—8624no—
251#127—24no—
252#127—8624no—
253#127—8624no—
254#127—864no—
255#124—8648no—
256#121—224no—
257#121—8648no—
258#121—8624no—
259C4×D4—8648no—
260C4×D4—8624no—
261C4×D4—8624no—
262C2×C4⋊C4—4312no—
263C2×C4⋊C4—436no—
264C2×C4⋊C4C22×D4316yes—
265C2×C22⋊C4—4312no—
266C2×C22⋊C4—4312no—
267C2×C22⋊C4—4312no—
268C2×C22⋊C4C22×D43112yes—
269C2×C42—24no—
270C2×C42—4324no—
271C2×C42—433no—
272C2×C42—433no—
273C2×C42—433no—
274C2×C42—433no—
275C2×C42—433no—
276C2×C42—436no—
277C2×C42—433no—
278C2×C42—8612no—
279C2×C42C22×D4313yes—
280C2×C42C22×D4311yescharacteristic
281C24—434no—
282C24C23×D4314yes—
283C24C23×D4311yescharacteristic
284#41—17264no—
285C2×Q8—8624no—
286C2×D4—224no—
287C2×D4—212no—
288C2×D4—212no—
289C2×D4—212no—
290C2×D4—8624no—
291C2×D4—8624no—
292C2×D4—8648no—
293C2×D4—8624no—
294C2×D4—8612no—
295C2×D4—8612no—
296C2×D4—8612no—
297C22×C4—26no—
298C22×C4—26no—
299C22×C4—4312no—
300C22×C4—433no—
301C22×C4—431no—
302C22×C4—431no—
303C22×C4—4312no—
304C22×C4—433no—
305C22×C4—434no—
306C22×C4—8624no—
307C22×C4—8612no—
308C22×C4—8624no—
309C22×C4D4×D43112yes—
310C22×C4C23×D4314yes—
311C22×C4C23×D4313yes—
312C22×C4C23×D4313yes—
313C4⋊C4—212no—
314C4⋊C4—8624no—
315C4⋊C4—8612no—
316C22⋊C4—224no—
317C22⋊C4—8624no—
318C22⋊C4—8624no—
319C22⋊C4—8624no—
320C42—26no—
321C42—4312no—
322C42—4312no—
323C42—4312no—
324C42—4312no—
325C42—4312no—
326C42—8612no—
327C42—866no—
328C42#1062190014yescomplemented
329C23—23no—
330C23—21no—
331C23—212no—
332C23—212no—
333C23—24no—
334C23—8612no—
335C23—8612no—
336C23—864no—
337C23C2×D4×D4316yes—
338C23C24×D4311yescharacteristic
339Q8—17216no—
340D4—416no—
341D4—424no—
342D4—17216no—
343D4—17248no—
344D4—17216no—
345D4—17224no—
346C2×C4—23no—
347C2×C4—23no—
348C2×C4—224no—
349C2×C4—212no—
350C2×C4—4316no—
351C2×C4—436no—
352C2×C4—436no—
353C2×C4—436no—
354C2×C4—4312no—
355C2×C4—436no—
356C2×C4—8624no—
357C2×C4—866no—
358C2×C4—8612no—
359C2×C4—17216no—
360C2×C4—17216no—
361C2×C4C2×D4×D4316yes—
362C2×C4C2×D4×D4316yes—
363C2×C4#41×D4316yes—
364C2×C4C2×#1062190016yes—
365C22—26no—
366C22—26no—
367C22—44no—
368C22—412no—
369C22—412no—
370C22—1724no—
371C22—17212no—
372C22—17212no—
373C22#127×D4314yes—
374C22C22×D4×D4313yes—
375C22C2×#41×D4313yes—
376C22C22×#1062190011yescharacteristic
377C4—26no—
378C4—44no—
379C4—434no—
380C4—434no—
381C4—4312no—
382C4—866no—
383C4—1724no—
384C4#14583444112yescomplemented
385C2—24no—
386C2—84no—
387C2—3444no—
388C2C2×#127×D4311yescharacteristic
389C2#532×D4313yes—
390C2C2×#1458344413yes—
subgroupG/H
center, FrattiniC23C24×D43
commutator, socle, cosocleC23×C43C25
FittingC43×#2856C2
hypercenter#2856D43
hypocenterC43#36644
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2856

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#14583444C2semidirect
2. #19142992C2semidirect
3. #19142989C2semidirect
4. #19142949C2semidirect
5. #19142940C2semidirect
6. #19142938C2semidirect
7. #127×Dic43C2semidirect
8. #19137159C2semidirect
9. #19137157C2semidirect
10. C2×C42×Dic43C2semidirect
11. C43×#2856C2semidirect
67. C2×C4×Dic43D4semidirect
120. C42×C43#41semidirect
132. C4×Dic43#41semidirect
160. C2×Dic43#127semidirect
184. C4×C43#532semidirect
189. Dic43#532semidirect
196. #2856D43semidirect
236. C43#36644semidirect
328. C42#10621900semidirect
384. C4#14583444semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#145834442
#191429922
#191429892
#191429492
#191429402
#191429382
#127×Dic432
#191371592
#191371572
C2×C42×Dic432
C43×#28562
#3664443